If the first shot is blank,should the prisoner ask for revolver to be spun or should they choose that it be shot again?

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In a certain society any time somebody commits a serious crime they must be shot at twice with a 6 bullet revolver. The revolver only has two bullets in it though, both of them right next to each other. They spin the revolver once and shoot the gun. If there was no bullet in that chamber they give the prisoner the option to either spin the chamber again or just shoot again.
If the first shot is a blank, should the prisoner ask for the revolver to be spun or should they choose that it be shot again?

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They should have them shoot again. If it is spun again there is a 2/6 chance they will get shot. There are four possible spots that don't have bullets and only one is followed by a bullet. This means that the chance is only 1/4 that they will be shot if they don't spin it.

You have a basketball hoop and someone says that you can play one of two games.
Game1 : You get one shot to make the hoop.
Game2 : You get three shots and you have to make two of three shots.
If p is the probability of making a particular shot, for which values of p should you pick Game1 or Game2?

Someone shows you two boxes and he tells you that one of these boxes contains two times as much as the other one, but he does not tell you which one this is. He lets you choose one of these boxes, and opens it. It turns out to be filled with $10. Now he gives you the opportunity to choose the other box instead of the current one (and skip the $10 of the first box), because the second box could contain twice as much (i.e. $20).

Should you choose the second box, or should you stick to your first choice to maximize the expected amount of money?

Welcome to the deadly game placed by the serial killer Jigsaw. You are tied to a chair and you cant move your hands or get up. Jigsaw shows you an empty gun with all the six chambers empty. He puts two bullets in the adjacent chambers and then close the barrel. He spins it and then point the gun to your head. The first shot snaps. It was an empty slot.

Now before pressing the trigger again, he asks you whether to pull the trigger or to spin the barrel first and then pull the trigger.

If the second shot goes empty, you will be spared by him. What will you choose?

Also think what will you chose if the bullets are not in the adjacent chambers.